The present invention relates in general to tuning musical instruments and, more particularly, to digital aural tuning of musical instruments having a plurality of adjustable frequency tone generators, such as strings in pianos, for generating a like plurality of musical notes. While the present invention is generally applicable to a variety of musical instruments including, for example, harpsichords, organs and pianos, it will be described herein with reference to tuning pianos for which it is particularly applicable and initially being applied.
Aural tuning techniques have been used to tune pianos since the earliest introduction of these instruments in the seventeen hundreds. In conventional aural tuning, a human tuner listens to a reference note and adjusts another note of the piano until that note sounds consonant with the reference note. Consonance can be indicated by a specified beat rate between the note being tuned and the reference note. Beat rate tuning is possible because an equally tempered scale is based upon simple mathematical relationships. In actuality, the frequencies which make up given notes of a piano and other instruments, do not correspond exactly to simple mathematic relationships.
For example, while "harmonics" denote integer multiples of a base frequency of a musical note, the overtones actually produced by a piano string are not harmonics and, to distinguish the overtones from harmonics, are called "partials". Each note of a piano includes a plurality of partials which are referred to as a "partial ladder" which can be used to represent all partials of a note or at least all partials which are required to tune an instrument. Partial ladders can be the relative pitches of the included partials for a note; however, more commonly they are listed as the deviation of the included partials from their corresponding harmonics and are quantified in "cents" where one cent is the amount of pitch difference that is equal to one per cent (0.01) of a semitone.
The difference between a given partial and its ideal harmonic is caused in part by "inharmonicity" which causes the partials of a vibrating piano string to be sharper or higher in frequency than would be expected from the harmonics for the string. Inharmonicity is due to the inherent stiffness of the metal wire which makes up the strings. While the inharmonicity theory presumes that all partials of a vibrating piano string are sharper than expected, in most instances, the partials may be either sharper, i.e., higher in frequency, or flatter, i.e., lower in frequency, than would be predicted by inharmonicity. This phenomenon, which is not accounted for by the inharmonicity theory and is believed to be due to the construction of the instrument, is referred to herein as "para-harmonicity". Every string or note of a piano can have a unique partial structure or partial ladder. To add to the complexity, each piano is different and even two pianos which are made side-by-side will require slightly different tuning or pitch for at least some and more often many of the notes of the pianos.
While manual aural tuning is the standard and produces excellent results, it is much more of an art than a science requiring substantial training of highly skilled and experienced persons. Further, manual aural tunings can vary from tuner to tuner and the manual aural tuning process can take a substantial amount of time. To reduce tuning time and the level of skill required for tuning instruments, other tuning techniques, such as tuning calculations, have been proposed. The concept of calculating a theoretical tuning for a piano has been known for many years, and was addressed widely in the Piano Technician's Journal and other publications throughout the 1970's and 1980's. The tuning calculations revolved around creating a perfect tuning using theoretical models. Unfortunately, the calculation techniques have not proven to be satisfactory since the calculations are very complex and the results do not match aural tuning results.
To improve upon the calculation techniques, measurement methods for determining the pitches of partials for the notes of an instrument to be tuned have been explored. One of the earliest attempts measured the difference between two partials of one note in the middle of the piano to determine the inharmonicity of the instrument. Unfortunately, the note chosen may or may not be representative of the notes around it and the measurements are time consuming and often inaccurate. This method is referred to as the partial-pair measurement method.
Another technique uses a calculated "inharmonicity constant" (Ic) which is derived from a physical measurement of the length and diameter of a vibrating string. This technique is referred to as the scale measurement method. Once the Ic is determined, equations including the Ic are used to calculate the partial structure for the notes of an instrument. A series of equations for calculating a tuning for 88 piano notes using an Ic were published in July, 1990 and further documented in the Piano Technician's Journal in 1991-1992. Unfortunately, this method requires scale measurements which normally take more time than the average aural tuner requires, around 2 hours, making it impractical.
Another scale measurement method is used in a product available from the inventor of the present application and sold under the trademark "Chameleon". In Chameleon, now Chameleon 1, the physical characteristics of five strings are measured to derive an Ic and then to calculate an 88 note tuning based on the Ic and equations which are somewhat simplified when compared to the equations found in the Piano Technician's Journal in 1991-1992.
Another technique measures the inharmonicity between two partials on each of three notes and calculates an 88 note tuning. This technique is an expansion of the partial-pair method mentioned above. Because the F, A and C notes are commonly used, this method is also referred to as the "FAC" method and is more fully described in U.S. Pat. No. 5,285,711. In this patent, the calculation of the 88 note tuning is performed using equations which rely on the Ic. The equations are either directly solved or utilized to prepare look-up tables which reduce the computing power required by a system embodying the invention. In either event, the calculations rely upon solution of the equations disclosed in the patent.
Unfortunately, all of the above methods presume that the inharmonicity theory is inviolate and that the inharmonicity constant (Ic) is accurately calculated by standard formulae, neither of which is true. The scale measurement methods use one of several standard formulae to convert wire type, diameter, and length into an inharmonicity constant (Ic). The partial-pair measurement methods use two measured partials of one or more notes, such as three notes, to calculate the inharmonicity constant with standard formulae. In either case, the inharmonicity constant determined is either not accurate or is not accurate for the entire instrument being tuned due, for example, to a failure to consider para-harmonicity.
Applicant's experience and research in aural, electronic measurement and calculated tuning has shown that the prior art tuning methods, while able to produce tunings that are acceptable to some tuners and musicians, are inadequate to produce tunings that rival the best aural human tuners. Expert aural tuners can detect pitch changes of as little as one-thousandth of a semitone, i.e., 0.1 cent again where one cent is the amount of pitch difference that is equal to one per cent (0.01) of a semitone. Such tuning precision is not within the capabilities of prior art techniques. Thus, if an expert aural human tuner is given enough time, he can produce a tuning that excels even the best prior art electronic or calculated tuning.
Accordingly, there is a need for an improved tuning method which can produce improved tuning results when compared to prior art methods. Preferably, the improved tuning method would not only produce improved instrument tunings but also would permit persons of less skill and experience than an expert aural tuner to produce improved instrument tunings in less time than either an expert aural tuner or a tuner using prior art tuning techniques. The tuning method would be further improved by use of an improved graphic and dynamic display of a pitch difference of an unknown pitch relative to a desired pitch which would provide highly accurate macro and micro tuning information in a single display.